Subgroups — C₂×C₅×SD₃₂ #65669

Order 320.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₈	C₂	1	1	yes	maximal, characteristic
3	C₅×SD₃₂	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×Q₈	—	2	1	no	—
6	C₂×C₅×D₄	—	2	1	no	—
7	C₅×Q₁₆	—	2	1	no	—
8	C₅×Q₁₆	C₂²	1	2	yes	complemented
9	C₅×D₈	—	2	1	no	—
10	C₅×D₈	C₂²	1	2	yes	—
11	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₅×C₁₆	C₂²	1	2	yes	complemented
13	C₂×SD₃₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂³×C₅	—	4	1	no	—
15	C₅×Q₈	—	2	2	no	—
16	C₅×Q₈	—	4	1	no	—
17	C₅×D₄	—	2	2	no	—
18	C₅×D₄	—	4	1	no	—
19	C₂×C₄×C₅	—	4	1	no	—
20	C₂×C₄×C₅	D₄	1	1	yes	characteristic
21	C₅×C₈	D₄	1	1	yes	characteristic
22	C₅×C₈	C₂³	1	1	yes	characteristic
23	C₂×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
24	C₂×D₈	C₂×C₅	1	1	yes	characteristic
25	SD₃₂	C₂×C₅	1	4	yes	direct product factor
26	C₂×C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
27	C₂²×C₅	—	4	2	no	—
28	C₂²×C₅	—	8	2	no	—
29	C₂²×C₅	D₈	1	1	yes	characteristic
30	C₄×C₅	—	4	2	no	—
31	C₄×C₅	D₈	1	1	yes	characteristic
32	C₄×C₅	C₂×D₄	1	1	yes	characteristic
33	C₂×Q₈	—	2	1	no	—
34	C₂×D₄	—	2	1	no	—
35	Q₁₆	—	2	1	no	—
36	Q₁₆	C₂²×C₅	1	2	yes	complemented
37	D₈	—	2	1	no	—
38	D₈	C₂²×C₅	1	2	yes	—
39	C₂×C₈	C₂²×C₅	1	1	yes	characteristic
40	C₁₆	C₂²×C₅	1	2	yes	complemented
41	C₂×C₅	—	8	2	no	—
42	C₂×C₅	SD₃₂	1	2	yes	direct product factor
43	C₂×C₅	C₂×D₈	1	1	yes	characteristic
44	C₂³	—	4	1	no	—
45	Q₈	—	2	2	no	—
46	Q₈	—	4	1	no	—
47	D₄	—	2	2	no	—
48	D₄	—	4	1	no	—
49	C₂×C₄	—	4	1	no	—
50	C₂×C₄	C₅×D₄	1	1	yes	characteristic
51	C₈	C₅×D₄	1	1	yes	characteristic
52	C₈	C₂³×C₅	1	1	yes	characteristic
53	C₅	C₂×SD₃₂	1	1	yes	characteristic, direct product factor, Sylow
54	C₂²	—	4	2	no	—
55	C₂²	—	8	2	no	—
56	C₂²	C₅×D₈	1	1	yes	characteristic
57	C₄	—	4	2	no	—
58	C₄	C₅×D₈	1	1	yes	characteristic
59	C₄	C₂×C₅×D₄	1	1	yes	characteristic
60	C₂	—	8	2	no	—
61	C₂	C₅×SD₃₂	1	2	yes	direct product factor
62	C₂	C₂×C₅×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	D₈
commutator, Frattini, cosocle	C₈	C₂³×C₅
prime radical	C₂×C₅×D₈	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₅×Q₁₆	C₂	semidirect
3. C₅×SD₃₂	C₂	direct (N × H)
4. C₂×C₅×C₁₆	C₂	semidirect
8. C₅×Q₁₆	C₂²	semidirect
12. C₅×C₁₆	C₂²	semidirect
13. C₂×SD₃₂	C₅	direct (N × H)
23. C₂×Q₁₆	C₂×C₅	semidirect
25. SD₃₂	C₂×C₅	direct (N × H)
26. C₂×C₁₆	C₂×C₅	semidirect
36. Q₁₆	C₂²×C₅	semidirect
40. C₁₆	C₂²×C₅	semidirect
42. C₂×C₅	SD₃₂	direct (N × H)
53. C₅	C₂×SD₃₂	direct (N × H)
61. C₂	C₅×SD₃₂	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×Q₁₆	2
C₂×C₅×D₈	2
C₅×SD₃₂	2
C₂×C₅×C₁₆	2
C₂×SD₃₂	5

Subgroups — C2×C5×SD32 #65669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×SD₃₂ #65669